Nonuniform Filter Banks Research Articles

Method for signal decomposition and denoising based on nonuniform cosine-modulated filter banks

In this paper, a novel method for signal decomposition and denoising is proposed based on a nonuniform filter bank (NUFB), which is derived from a uniform filter bank. With this method, the signal is firstly decomposed into M subbands using a uniform filter bank. Then according to their energy distribution, the corresponding consecutive filters are merged to compose the nonuniform filters. With the resulting NUFB, the signal can be readily matched and flexibly decomposed according to its power spectrum distribution. As another advantage, this method can be used to detect and remove the narrow-band noise from the corrupted signal. To verify the proposed method, a simulation of extracting the main information of an audio signal and removing its glitch is given.

On characterization of linear phase nonuniform filter banks

In this paper, a condition termed as linear phase condition (LPC), which ensures that the filters of a nonuniform filter bank are linear phase, is presented. It is observed that the proposed LPC is also applicable to the uniform filter bank case. Further, the utility of this LPC to find (i) necessary restrictions on the filters lengths, (ii) the number of symmetric and antisymmetric filters in the filter bank and (iii) filter bank decimation factors is also investigated. The results obtained for the different cases are also presented in the form of tables. These tables will facilitate the design of nonuniform filter bank by ruling out the non-solvable cases and by reducing the search space, thus saving the designers’ precious time.

Representations of Linear Dual-Rate System Via Single SISO LTI Filter, Conventional Sampler and Block Sampler

In this brief, it is proved that a linear dual-rate system can be represented via a series cascade of: 1) a conventional expander, a single-input single-output (SISO) linear time-invariant (LTI) filter and a block decimator, or 2) a block expander, an SISO LTI filter and a conventional decimator. Hence, incompatible nonuniform filter banks could achieve perfect reconstruction via LTI filters, conventional samplers and block samplers without expanding the input-output dimension of a subsystem of linear dual-rate systems or converting the nonuniform filter banks to uniform filter banks. The main advantage of the proposed representations is to avoid complicated design of the circuit layout caused by connecting subsystems with large input-output dimension or a lot of subsystems together.

Considering a Non-Uniform Filter Bank in an UWB Multi Band On-Off Keying Transceiver

Ultra Wide Band (UWB) wireless systems based on impulse radio have the potential to provide very high data rates over short distances. One of the solutions for the UWB communication systems is the Multi Band On-Off Keying (MB-OOK) which consists in an OOK modulation generalized over multiple frequency sub-bands and associated with a demodulation based on a non-trivial energy threshold comparison. This article presents the analysis and simulations of an UWB MB-OOK transceiver in the 6-8.5GHz band. This study is focused on the bandpass filter bank in the transceiver’s architecture. The use of a Bulk Acoustic Wave (BAW) filter bank in the transceiver is considered. Finally, system performance is estimated for the proposed architecture.

Low-Delay Nonuniform Pseudo-QMF Banks With Application to Speech Enhancement

This paper presents a method for designing low-delay nonuniform pseudo quadrature mirror filter (QMF) banks. This method is motivated by the work of Li, Nguyen, and Tantaratana, in which the nonuniform filter bank is realized by combining an appropriate number of adjacent sub-bands of a uniform pseudo-QMF bank. In prior work, the prototype filter of the uniform pseudo-QMF bank was constrained to have linear phase and the overall delay associated with the filter bank was often unacceptably large for filter banks with a large number of sub-bands. This paper proposes a pseudo-QMF filter bank design technique that significantly reduces the delay by relaxing the linear phase constraints. An example in which an oversampled critical-band nonuniform filter bank is designed and applied to a two-state modeling speech enhancement system is presented in this paper. Comparison of the performance of this system to competing methods employing tree-structured, linear phase multiresolution analysis indicates that the approach described in this paper strikes a good balance between system performance and low delay

Efficient dynamic channeliser based on nonuniform filter banks

AbstractIn the multi‐standard communications systems, the intermediate frequency (IF) signal usually consists of several subband signals with nonequal bandwidths and arbitrary band locations, and in some special cases the number, location and bandwidth of the subband signal are dynamically changeable during receiving. This paper presents an efficient architecture based on nonuniform filter banks to channelise these signals. The nonuniform filter bank can be constructed by directly merging the relevant uniform cosine‐modulated filter bank (CMFB) according to the nonuniform matrix. The whole filter design can be boiled down to design a prototype filter that meets some constraints. The proposed structure can be optimised to reduce the computational complexity using the relationships among different decimation factors of different subband signals. Along with signals dynamically changing, new channelisation can be implemented as long as updating the nonuniform matrix. New structure is provided with low cost in hardware and high flexibility. Simulation results are also presented to illustrate its feasibility. Copyright © 2007 John Wiley & Sons, Ltd.

Design of nonuniform cosine-modulated filter-banks with the perfect-reconstruction property and arbitrary filter lengths

Abstract In this paper' a method is proposed to construct recombination nonuniform cosine-modulated filter banks (CMFBs) with a perfect-reconstruction property and with arbitrary filter lengths. In this filter bank (FB) structure, certain channels of an original M-channel uniform FB are merged by a set of transmultiplexers (TMUXs), yielding nonuniform outputs, and the length restrictions on the original CMPB and the recombination TMUKs are avoided, allong them to have arbifrary filter lengths. By imposing certain improved matching conditions on the protote filters, nonuniform FBs with arbitrary filter lengths and with good properties can be obtained. As a result, the flexibility of selecting modulation types and filter lengths is greatly increased in the design of recombination nonuniform CMFBs. Another benefit due to the flexibility is that the system delay can be reduced. *Supported by National Natural Science FoLndation of China (Grant Nos. 60672125 and 60372047)

Oversampled nonuniform filter banks using quadratic optimisation and transition filters

A new approach to nonuniform filter bank design is introduced. The designed filter bank is composed of many different uniform sections which are joined together by transition filters. Oversampled complex modulated uniform filter banks are calculated by means of quadratic optimisation. This way, analysis and synthesis stages are designed separately, each one fulfilling its own set of constraints. Later on, uniform sections with different frequency resolutions are joined together by transition filters. The results show that the designed filter bank exhibits nearly perfect reconstruction behaviour. An example with frequency resolution similar to the first 18 critical bands is implemented.

Design of Nonuniform Filter Bank Transceivers for Frequency Selective Channels

In recent years, there has been considerable interest in the theory and design of filter bank transceivers due to their superior frequency response. In many applications, it is desired to have transceivers that can support multiple services with different incoming data rates and different quality-of-service requirements. To meet these requirements, we can either do resource allocation or design transceivers with a nonuniform bandwidth partition. In this paper, we propose a method for the design of nonuniform filter bank transceivers for frequency selective channels. Both frequency response and signal-to-interference ratio (SIR) can be incorporated in the transceiver design. Moreover, the technique can be extended to the case of nonuniform filter bank transceivers with rational sampling factors. Simulation results show that nonuniform filter bank transceivers with good filter responses as well as high SIR can be obtained by the proposed design method.

Efficient Algorithm for Solving Semi-Infinite Programming Problems and Their Applications to Nonuniform Filter Bank Designs

An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

A practical approach for the design of nonuniform lapped transforms

We propose a simple method for the design of lapped transforms with nonuniform frequency resolution and good time localization. The method is a generalization of an approach previously proposed by Princen, where the nonuniform filter bank is obtained by joining uniform cosine-modulated filter banks (CMFBs) using a transition filter. We use several transition filters to obtain a near perfect-reconstruction (PR) nonuniform lapped transform with significantly reduced overall distortion. The main advantage of the proposed method is in reducing the length of the transition filters, which leads to a reduction in processing delay that can be useful for applications such as real-time audio coding.

Design of linear-phase recombination nonuniform filter banks

This correspondence proposes a novel method for designing a class of recombination nonuniform filter banks (RNFBs) with the linear-phase (LP) property. In the structure of the proposed nonuniform filter bank (FB), certain channels of an M-channel uniform FB are merged by synthesis filters of transmultiplexers (TMUXs), yielding nonuniform subbands. By a detailed analysis of the frequency characteristics of the RNFBs, we derive the existence and matching conditions that are necessary for constructing the proposed RNFBs having good frequency responses. With those conditions being satisfied, the design problem becomes that of a set of LP uniform FBs. By using the Parks-McClellan algorithm, we are able to design the near-perfect-reconstruction LP RNFBs in a very simple and efficient way as demonstrated by two examples

Biorthogonal Recombination Nonuniform Cosine-Modulated Filter Banks and their Multiplier-Less Realizations

This paper studies the theory, design and multiplier-less (ML) realization of a class of perfect reconstruction (PR) low-delay biorthogonal nonuniform cosine-modulated filter banks (CMFBs). It is based on a recombination (or merging) structure previously proposed by the authors. By relaxing the original CMFB and the recombination transmultiplexer (TMUX) in the recombination structure to be biorthogonal, nonuniform CMFBs with lower system delay can be obtained. This also increases the possible choices of the prototype filters to meet different design objectives. A matching condition is introduced to suppress the spurious response resulting from the mismatch in the transition bands of the two biorthogonal CMFBs. A complete factorization of biorthgonal CMFB using the lifting scheme is employed to obtain structurally PR biorthogonal nonuniform filter banks (FBs), which are robust to coefficient quantization. In addition, by approximating the lifting coefficients and the modulation matrices by the sum of powers-of-two (SOPOT) coefficients, ML realization with very low implementation complexity is obtained. Design examples and comparison are given to illustrate the effectiveness of the proposed method.

A computationally efficient nonuniform FIR digital filter bank for hearing aids

A computationally efficient nonuniform digital FIR filter bank is proposed for hearing aid applications. The eight nonuniform spaced subbands are formed with the help of frequency-response masking technique. Two half-band finite-impulse response (FIR) filters are employed as prototypes resulting in significant improvements in the computational efficiency. We show, by means of example, that an eight-band nonuniform FIR filter bank with stopband attenuation of 80 dB can be implemented with 15 multipliers. The performance of the filter bank is enhanced by optimizing the gains for each subband. The tests on various hearing loss cases suggest that the proposed filter achieves reasonable good matching between audiograms and magnitude responses of the filter bank at very low computational cost.

Audio coding and image denoising based on the nonuniform modulated complex lapped transform

Xiong and Malvar recently introduced a nonuniform modulated complex lapped transform (NMCLT) with good time-localization and controllable frequency resolution by using an oversampled nonuniform filter bank to generate its real and the imaginary components. In this paper, we first show that oversampling in the NMCLT is not necessary in theory but a by-product of fast implementation in practice. We also point out that the amount of oversampling, which can be flexibly controlled, depends on the application. We then describe in detail the implementation of the inverse transform, which was not addressed clearly by Xiong and Malvar. We present the first applications of the NMCLT to audio coding and image denoising. A scalable audio coder has been implemented by controlling the amount of oversampling and exploiting redundancy among the NMCLT coefficients via predictive coding. Experimental results show that the audio coder reduces pre-echoes and improves the sound quality of audio clips with transient sounds. A simple denoising algorithm based on the NMCLT has also been devised to provide images with better visual quality than those obtained with wavelet-based soft thresholding.

Design of perfect-reconstruction nonuniform recombination filter banks with flexible rational sampling factors

This paper studies the design of a class of perfect-reconstruction (PR) nonuniform filter banks (FBs) called recombination nonuniform FBs (RNFBs). They are constructed by merging subbands in a uniform FB with sets of transmultiplexers (TMUXs). It generalizes the RNFBs previously proposed by the authors to allow more general choice of the sampling factors. The spectral inversion and spurious response suppression problems of these new RNFBs using cosine modulation are analyzed, and a simple design method based on a matching condition is proposed. It is also found that the FB and the TMUX in the recombination structure can be designed separately to satisfy the matching condition. In addition, real-time adaptive merging of the channels to provide dynamic nonuniform frequency partitioning is feasible. Another advantage of the RNFBs is that the recombination and processing of the subband signal can be done at the decimated domain of the uniform FB, which greatly reduces its implementation complexity. Design examples show that high quality nonuniform PR FBs with low implementation complexity and variable time-frequency resolution can be obtained by the proposed method.

The Theory and Design of a Class of Recombination Nonuniform Filter Banks with Linear Phase Filters

This paper proposes a new theory and design method for a class of recombination nonuniform filter banks (RNFBs) with linear phase (LP) filters. In a uniform filter bank (FB), consecutive channels are merged by sets of transmultiplexers (TMUXs) to realize a nonuniform FB. RNFBs with LP analysis/synthesis filters are of great interest because the analysis filters for the partially reconstructed signals, through merging, are LP and hence less phase distortions are introduced to the desired signals. We analyze the spectrum supports of the analysis filters of these LP RNFBs. The conditions on the uniform FB and recombination TMUXs of an LP RNFB with good frequency characteristics are determined. These conditions are relatively simple to be satisfied and the uniform FB and recombination TMUXs can be designed separately without much degradation in performance. This allows dynamically recombination of different number of channels in the original uniform FB to give a flexible and time-varying frequency partitioning. Using these results, a method for designing a class of near-perfect-reconstruction (NPR) LP RNFBs with cosine roll-off transition band using the REMEZ algorithm is proposed. A design example is given to show that LP RNFBs with good frequency responses and reasonably low reconstruction errors can be achieved.

Constituent subband allocation for system modeling nonuniform subband adaptive filters

Subband adaptive filters (SAFs) have gained widespread use in key applications such as echo cancellation, system identification, and equalization. SAFs are normally constrained to utilize uniform filterbanks. However, it has been recently proposed that nonuniform filterbanks can give additional flexibility to SAFs that may be used to increase performance. A rigorous mean square error (MSE) analysis has also been completed for standard system modeling nonuniform SAF configurations. This paper completes the next step by theoretically deriving an adaptive algorithm to control the nonuniform filterbank for a system modeling SAF. The algorithm is constructed so that MSE, convergence time, and computational complexity are minimized. Two numerical simulations compare the nonuniform SAF adaptive filterbank algorithm to standard, equivalent uniform SAF performance.

A two-channel nonuniform perfect reconstruction filter Bank with irrational down-sampling factors

Most of the existing methods designed to implement fractional interpolation and decimation are limited by rational scaling factors such as L/M, where L and M are positive integers. The general procedure is usually done with up-sampling by L first, and then followed by down-sampling by M. This scheme, however, requires two steps and higher sampling rates to fulfill and is not capable in dealing with irrational scaling factors, which cannot be represented by L/M. We propose a new method to solve the above two difficulties by a single step. Furthermore, a new structure of a two-channel nonuniform perfect reconstruction filter bank is derived using this new method, and the experimental results are presented.

Mean square error analysis of nonuniform subband adaptive filters for system modeling

Nonuniform filterbanks have recently been proposed for subband adaptive filters (SAFs). However, nonuniform SAFs have not yet been given a thorough performance analysis. This paper gives a comprehensive mean square error (MSE) analysis of system modeling, nonuniform (and, degeneratively, uniform) SAFs after convergence for a specified filterbank. Using the equivalent polyphase representation suggested by Ono et al., minimum MSE (MMSE) estimates for the individual subband errors are presented with respect to a given filterbank for finite length (FIR), infinite length causal (IIR), and infinite noncausal adaptive filters. Using these subband MMSE estimators, an MMSE estimator is derived for the overall fullband error. Finally, the derived MMSE estimators are verified by a numerical simulation. The intent of this paper is not to compare nonuniform and uniform SAF performance but merely to present a unified mathematical methodology to predict their MMSEs.